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<title id="title">An Introduction to Electronics</title>
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<div id="topnav">PHY342: An Introduction to electronics</div>
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<div id="main"><h1>Superposition theorem</h1>
<p>Superposition theorem states that a network containing several voltage sources may be analysed by considering the effect of each source in turn. Simply by changing the voltage source with a resistor that has a value of internal resistance. 
The total current on the component is equal to algebraic sum of all currents obtained from different sources.</p>
<p>The simple example will be considered to represent this theory.</p>
<p>A circuit consists of two voltage sources (bateries) with internal resistance of 2 and 3 ohms respectively and a light bulb with a resistance of 50 ohms. Bateries supply 5 V each. What is the current that flows through the bulb ?</p>
<p class="centre">
<img alt="Superposition" src="../resources/sup_1.jpg" /> </p>
<p>Using Superposition Theorem, we will find the current produced by first baterry.
Replace the second batery with a resistor. The simplyfied circuit becomes:</p>
<p class="centre">
<img alt="Superposition" src="../resources/sup_2.jpg" /> </p>
<p>From the circuit above we can see that there is one resistor in series and another two in paralel.</p>
<p>Total resistance of the circuit is given by </p>
<p><img alt="equation" class="block" src="http://bricefernandes.com/cgi-bin/mimetex.cgi?R_t=R_2+%5Cfrac{R_bR_3}{R_b+R_3}=4.83%5Cgama"></img></p>
<p>The current through bulb (<img alt="equation" class="inline" src="http://bricefernandes.com/cgi-bin/mimetex.cgi?R_b"></img>) can be found using potential divider </p>
<p><img alt="equation" class="block" src="http://bricefernandes.com/cgi-bin/mimetex.cgi?V_b=%5Cfrac{V}{R_t} R_p"></img> </p>
<p>So <img alt="equation" class="inline" src="http://bricefernandes.com/cgi-bin/mimetex.cgi?I_b=%5Cfrac{V_b}{R_b}"></img>  and   <img alt="equation" class="inline" src="http://bricefernandes.com/cgi-bin/mimetex.cgi?I_b=0.0586 A"></img> </p>
<p>Now lets consider different batery. Performing same simplifications our circuit becomes:</p>
<p class="centre">
<img alt="Superposition" src="../resources/sup_3.jpg" /> </p>
<p>And the current passing through the bulb is <img alt="equation" class="inline" src="http://bricefernandes.com/cgi-bin/mimetex.cgi?I_b=0.04 A"></img></p>
<p>Then according to superposition theory the total current that passes through light bulb is equal to </p>
<p><img alt="equation" class="block" src="http://bricefernandes.com/cgi-bin/mimetex.cgi?I=I_1+I_2=0.098 A"></img></p>
<p>If resistance and the current are known, the voltage across this bulb can be easily calculated using Ohm's Law.</p></div>

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